Re: how

Liste des GroupesRevenir à s math 
Sujet : Re: how
De : moebius (at) *nospam* example.invalid (Moebius)
Groupes : sci.math
Date : 22. Apr 2024, 19:34:02
Autres entêtes
Organisation : A noiseless patient Spider
Message-ID : <v06ais$13k2s$1@dont-email.me>
References : 1 2 3 4 5 6 7 8 9 10 11 12
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Am 22.04.2024 um 20:20 schrieb Moebius:
Am 22.04.2024 um 19:53 schrieb WM:
Le 22/04/2024 à 19:27, Moebius a écrit :
>
A /countable set/ S (as defined in the context of set theory) is NOT "countable" because it can be counted (and/or there is someone who can count its elements), but because there is an injective function f such that f maps IN onto S.
>
Why can't it be counted?
 Because we finite beings (except of Chuch Norris of course) cannot count infinitely many object, that's why, Mückenheim.
On the other hand, "in principle" it might be "possible" - if you believe in/accept supertasks.
See: https://en.wikipedia.org/wiki/Supertask
Note that set theory does not rely on supertasks. That's why we use a set theoretic definition for the notion /countable set/. See above.
Hint: On this basis we can prove for example (a) that the set of rational numbers (Q) is a countable set and (b) that the set of real numbers (R) is an uncountable set.

Date Sujet#  Auteur
24 Mar 24 * V1414WM
24 Mar 24 +* Re: V20Chris M. Thomasson
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